Multi-stable transitions of Turing patterns induced by disturbances and the evolution law of configurational entropy

Turing pattern systems exhibit prominent multistability, yet most existing studies on pattern transitions rely on tuning system parameters—an approach impractical for scenarios with fixed parameters. To clarify how external disturbances switch coexisting stable patterns under constant parameters, this study adopts three classic reaction–diffusion models including one discrete-time and two continuous-time models, combined with stability analysis and numerical simulations. Spatial noise is utilized as external disturbance, and spectral configurational entropy is introduced to quantify pattern spatial order. The results verify the existence of Turing instability in the systems. External disturbances can trigger unidirectional transitions of various coexisting Turing patterns toward labyrinthine structures, and such structural evolutions follow the principle of configurational entropy growth. Labyrinth patterns are high-entropy stable attractors with stronger structural robustness. This work investigates disturbance-controlled Turing pattern switching under fixed-parameter conditions, and provides quantitative insights and theoretical references for self-organized pattern manipulation across multiple disciplines.